About Equations of Lines:

We often need to write the equation of a line in different forms. The slope-intercept form can be obtained by solving a linear equation in two variables for y. This gives us y = mx + b, where m is the slope and the y-intercept occurs at (0,b). In some cases, we will not be given enough information to immediately put a line in slope-intercept form. For these scenarios, we are often given a slope and a point on the line or two points on the line and no slope. When this occurs, we can use the point-slope form. This form y - y1 = m(x - x1) allows us to plug in the known point for (x1,y1) and our known slope m and obtain our slope-intercept form by solving for y. Lastly, we will run into standard form. With standard form, the definition varies from textbook to textbook. Essentially, we see standard form as: ax + by = c, where a, b, and c are integers and a is non-negative. Again this could be relaxed to say a, b, and c are just real numbers. When working with an equation in standard form, we can see that the slope occurs at: m = -a/b and our y-intercept occurs at: y-int: (0, c/b).


Test Objectives
  • Demonstrate the ability to write the equation of a line in slope-intercept form
  • Demonstrate the ability to write the equation of a line in point-slope form
  • Demonstrate the ability to write the equation of a line in standard form
Equations of Lines Practice Test:

#1:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}m=\frac{1}{2}, (0,-3)$$

$$b)\hspace{.2em}m=0, (0,-4)$$


#2:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}m=-2, (1,0)$$

$$b)\hspace{.2em}m=\frac{3}{2}, (2,4)$$


#3:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}m=1, (2, -2)$$

$$b)\hspace{.2em}(5,-4), (5, 3)$$


#4:

Instructions: write in standard form.

$$b)\hspace{.2em}(0,3), (5,0)$$

$$a)\hspace{.2em}(0,0), (-1,-3)$$


#5:

Instructions: write in slope-intercept form.

$$a)\hspace{.2em}(-5,-4),(4,0)$$

$$b)\hspace{.2em}(0,-4),(-3,0)$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}y=\frac{1}{2}x - 3$$

$$b)\hspace{.2em}y=-4$$


#2:

Solutions:

$$a)\hspace{.2em}y=-2x + 2$$

$$b)\hspace{.2em}y=\frac{3}{2}x + 1$$


#3:

Solutions:

$$a)\hspace{.2em}y=x - 4$$

$$b)\hspace{.2em}x=5$$


#4:

Solutions:

$$a)\hspace{.2em}3x + 5y=15$$

$$b)\hspace{.2em}3x - y=0$$


#5:

Solutions:

$$a)\hspace{.2em}4x - 9y=16$$

$$b)\hspace{.2em}4x + 3y=-12$$